In may our children's primary school in Islington, inner north London, held a fund-raiser. This was no bingo night.
In a celebrity auction of "time and talents", Coldplay singer Chris Martin agreed to visit a family's house and play a song or two on their piano. A family paid £5000 ($A12,500) for the privilege.
The school was able to put Martin under the hammer because his business manager has a child there. So does Labour's Schools Minister, Lord Adonis, who offered a tour and cup of tea at the House of Lords. That was bought by the night's auctioneer, Tory MP and former Spectator editor Boris Johnson, also a parent at the school. His little cross-party joke cost £5000.The night provoked snorts of derision in the national press - Islington is often lampooned as the home of media types, chattering classes and so on - but it raised a whopping £43,000. It also showed the school's great divide. Half the parents have amazing cultural capital; many of the rest could not have afforded the £10 entry fee.
In Islington, "half the people are very rich and the other half are on benefits, and there's no one in between", says our neighbour, a senior executive at the borough council. He exaggerates, but not by much. It is one of the most socially diverse boroughs in Britain. And in some respects it reminds me of the inner suburbs of Melbourne.
About a quarter of Islington's population is non-white. It was well-heeled in the 19th century, declined in the 20th and began gentrifying in the 1980s. It has great disparities of wealth: mansions that hold a family of four stand near council housing estates that hold 400. Its main street, Upper Street, is choked with cafes and restaurants. It is Fitzroy on steroids.
Of course, Fitzroy's racial make-up is different and the income divide not as great. And inner London retains a sizeable white working class so the link between ethnicity and income is not neat, though they often converge. The main parallel is that about a quarter of south Fitzroy's population is in public housing. If not for that housing, real estate in inner Melbourne and Islington is now so expensive that both areas would be ethnically almost uniform and virtually all middle class.
Low-income housing exists across London, even in posh areas such as Bayswater and Chelsea. It is one of the city's most striking features. But leaving aside platitudes about the joys of diversity, does mixing do anyone any good? Does an integrated neighbourhood give people of all classes and colours a better life?
Once I would have unhesitatingly said yes. But living here, I see that however close they live to each other, the classes don't mingle. In our street, the well-off and low-income homes keep to themselves (public housing includes many single houses as well as estates). And while there is some mixing at our school, children, sadly, tend not to cross class lines.
Still, a case can be made that integration works better. Recent research suggests that both high rates of outmarriage among British Afro-Caribbeans (50 and 35 per cent for men and women respectively) and a growing propensity to live in integrated neighbourhoods, are improving rates of social mobility.
Conversely, reports identified deep-rooted segregation in the northern cities of Bradford and Oldham as the cause of race riots in 2001.
Over in Marseilles, there were almost no riots last year, while the suburbs of other French cities burned.
Marseilles is poor but unusually well integrated. It has known migration for longer than much of France. And, according to the New York Times, because it is bounded by hills that are hard to build on, low-income housing has had to be mixed into the existing city, not pushed to the fringe as it has been elsewhere in France.
These snippets alone do not make the case for integration.
Observer columnist Nick Cohen said our school's auction exposed Islington's "educational apartheid," side by side but apart. But if nothing else, the funds raised will go to an IT centre for the benefit of all students. The money is going into the state system.
At the end of primary school, though, apartheid really kicks in. Most middle-class children leave the area, for private or selective state schools. The working class is stuck in local high schools with Blackboard Jungle reputations.
Academics argue furiously about whether segregation is growing in Britain. There are certainly worrying signs, especially in Pakistani communities in the north.
Yet the picture is complicated. London is becoming one of Europe's most racially mixed cities. It was evident in the faces of the dead and of the people who mourned them after last year's bombings. That extraordinary mingling was an answer, people said, to the separateness that helps to produce terrorism.
Of course, the new diversity masks older divisions. While the global middle class of all colours mixes increasingly comfortably with itself, Islington and Fitzroy suggest that wealth - perhaps even more than race - remains the big chasm.
Research by geographer Mike Poulsen shows that Australian suburbs may be the least ethnically segregated in the West. But the wealth divide grows by the day.
One or two British cities have started school twinning programs, to mix children of different backgrounds for some activities. It is a good idea, albeit a small one.
While education remains the best hope for integration, increasingly divided school systems show how much we stand to lose.
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